Apparatus and method for reconstruction of volumetric images in a divergent scanning computed tomography system

ABSTRACT

An apparatus and method for reconstructing image data for a region are described. A radiation source and multiple one-dimensional linear or two-dimensional planar area detector arrays located on opposed sides of a region angled generally along a circle centered at the radiation source are used to generate scan data for the region from a plurality of diverging radiation beams, i.e., a fan beam or cone beam. Individual pixels on the discreet detector arrays from the scan data for the region are reprojected onto a new single virtual detector array along a continuous equiangular arc or cylinder or equilinear line or plane prior to filtering and backprojecting to reconstruct the image data.

RELATED APPLICATIONS

This application is a continuation of U.S. application Ser. No.10/645,323, filed Aug. 21, 2003, now U.S. Pat. No. 7,106,825 whichclaims the benefit of U.S. Provisional Application No. 60/405,096, filedAug. 21, 2002. The entire teachings of the above applications areincorporated herein by reference.

BACKGROUND OF THE INVENTION

The present invention relates generally to 2D and 3D computerizedtomography (CT). In particular this invention relates to methods andsystems for reconstructing projection data which are neither equlinearor equiangular in nature.

In conventional computerized tomography for both medical and industrialapplications, an x-ray fan beam and an equilinear or equiangular arraydetector are employed. Two-dimensional (2D) axial imaging is achieved.While the data set is complete and image quality is correspondinglyhigh, only a single slice of an object is imaged at a time. When a 3Dimage is acquired, a “stack of slices” approach is employed. Acquiring a3D data set one slice at a time is inherently slow. Moreover, in medicalapplications, motion artifacts occur because adjacent slices are notimaged simultaneously. Also, dose utilization is less than optimal,because the distance between slices is typically less than the x-raycollimator aperture, resulting in double exposure to many parts of thebody.

In a system employing true cone-beam geometry, a cone-beam x-ray sourceand a flat 2D equilinear or curved 2D equiangular area detector areemployed. An object is scanned, preferably over a 360-degree range,either by moving the x-ray source in a scanning circle around the objectwhile keeping the 2D area detector fixed with reference to the source,or by rotating the object while the source and detector remainstationary. In either case, it is the relative movement between thesource and object which affects scanning. Compared to the 2D “stack ofslices” approach for 3D imaging, the cone-beam geometry has thepotential to achieve rapid 3D imaging of both medical and industrialobjects, with improved dose utilization.

The cone-beam geometry for 3D imaging has been discussed extensively inthe literature, as represented by the following: M. Schlindwein,“Interactive Three-Dimensional Reconstruction from Twin Cone-BeamProjections”, IEEE Trans Nucl.Sci., Vol. NS-25, No. 5, pp. 1135-1143(October 1978); Gerald N. Minerbo, “Convolutional Reconstruction fromCone-Beam Projection Data”, IEEE Trans. Nucl.Sci., Vol. NS-26, No. 2,pp. 2682-2684 (April 1979); Heang K. Tuy, “An Inversion Formula forCone-Beam Reconstruction”, SIAM J. Math, Vol. 43, No. 3, pp. 546-552(June 1983); L. A. Feldkamp, L. C. Davis, and J. W. Kress, “PracticalCone-Beam Algorithm”, J. Opt. Soc. Am. A., Vol. 1, No. 6, pp. 612-619,(June 1984); Bruce D. Smith, “Image Reconstruction from Cone-BeamProjections: Necessary and Sufficient Conditions and ReconstructionMethods”, IEEE Trans. Med. Imag., Vol. MI-44, pp. 14-24 (March 1985);and Hui Hu, Robert A. Kruger, and Grant T. Gullberg, “QuantitativeCone-Beam Construction”, SPIE Medical Imaging III: Image Processing,Vol. 1092, pp. 492-501 (1989).

Several methods for collecting cone beam data have been developed. Onetechnique involves acquiring volumetric image data using a flat panelmatrix image receptor, as described in U.S. Pat. No. 6,041,097 to Roos,et al. Another method uses image intensifier-based fluoroscopic camerasmounted on a CT-gantry type frame. Such a system is described in a paperpresented at SPIE Medical Imaging Conference on Feb. 24, 1997, by R.Ning, X. Wang, and D. L. Conover of Univ. of Rochester Medical Center.

U.S. Pat. No. 5,319,693 to Eberhard, et al. discusses simulating arelatively large area detector using a relatively small area detector byeither moving the actual area detector relative to the source, or movingthe object relative to the detector.

However, there is a significant limitation of cone-beam reconstructionwhen individual flat detectors are reconstructed independently. Simplycombining separate reconstructed portions of the object fromindependently processed projections results in an image characterized bydiscontinuous jumps between the various projections. Alternatively, onecould first combine the discreet data sets from each detector into a newsingle data set that is then reconstructed. However, by simply combiningthe data into a larger data array and performing standard reconstructiontechniques, the data elements in the new data set are not equallyspaced. Thus, the resultant images will be distorted geometrically, orthe dynamic range of the reconstructed data set will not represent thetrue transmission values of the object being imaged.

SUMMARY OF THE INVENTION

The deficiencies in existing methods for combining image data frommultiple flat panel detector arrays result from the fact that thesedetector arrays have neither equilinear nor equiangular geometries. Thepresent invention relates to improved systems and methods forreconstructing projection data, including x-ray projection data fortwo-dimensional (2D) fan-beam and three-dimensional (3D) cone beam CTimaging, in which the geometry of the detectors is neither equilinear orequiangular, by reprojecting the actual measured data into a new virtualdata array, which has an equilinear or equiangular geometry. In oneaspect, multiple discreet projection data sets, which, when combined,are neither equilinear or equiangular, are reprojected into a newvirtual data set on an equilinear spaced detector on a line or plane, oran equiangular spaced detector array on an arc or cylinder. Theresulting virtual projection data set can then be reconstructed usingstandard backprojection techniques and generate images which aregeometrically correct, and represent the true x-ray transmissionproperties of the object being imaged.

In one embodiment, the projection data from two or more 1D linear or 2Dflat detector arrays are reprojected onto a single equilinear orequiangular virtual detector array prior to filtering and backprojectingthe projection data.

In another embodiment, the projection data from two or more discretedetector positions are reprojected onto a virtual detector array havingan equilinear or equilangular configuration, and the reprojected data isreconstructed to provide an image.

The “virtual” detector array of the present invention is a data arraycomprising a plurality of pixels, having an equiliner or equiangulargeometry, where the data values assigned to each pixel in the virtualarray is based upon data from an actual detector or set of detectorshaving a non-equilinear and non-equiangular geometry.

The present invention advantageously allows for the 2D and 3Dtomographic reconstruction of objects. This invention enables divergentx-ray 2D fan beam or 3D cone beam tomographic reconstruction using adiscrete number of 1D linear or 2D flat detectors angled relative to oneanother by using a novel rebinning and reprojection technique ontovirtual equilinear or equiangular detector arrays prior to performingstandard filtered backprojection tomographic reconstruction techniques.

The present invention is particularly useful for medical imagingapplications, as well as numerous industrial applications, such astesting and analysis of materials, inspection of containers, and imagingof large objects.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features and advantages of theinvention will be apparent from the following more particulardescription of preferred embodiments of the invention, as illustrated inthe accompanying drawings in which like reference characters refer tothe same parts throughout the different views. The drawings are notnecessarily to scale, emphasis instead being placed upon illustratingthe principles of the invention.

FIG. 1 shows standard equilinear and equiangular geometries used invarious generations of CT scanners;

FIG. 2 shows a standard equilinear detector geometry in which thedetectors are arranged with constant spacing along a line or plane;

FIG. 3 shows the radiation profile of an imaged object defined by anequilinear arrangement of detectors;

FIG. 4 shows a standard equiangular detector geometry in which thedetectors are arranged with constant angular spacing along an arc orcylindrical surface;

FIG. 5 shows the radiation profile of an imaged object defined by anequiangular arrangement of detectors;

FIG. 6 shows three equilinear-spaced detector arrays positioned andangled relative to one another, resulting in a geometry that is neitherequilinear nor equiangular;

FIG. 7 shows the predicted radius of reconstructed object with threedetector arrays generally positioned along an arc having a radiuscentered at the x-ray focal spot;

FIG. 8 shows the predicted radius of reconstructed object with three 1Dlinear or 2D flat plate detector arrays positioned along a straight linein an equilinear arrangement;

FIG. 9 is a flow chart diagram of the rebinning algorithm forreconstructing 1D fan beam or 2D cone beam projection data which isneither equilinear or equiangular;

FIG. 10 shows the projection of multiple angled detector array positionsonto a single virtual flat equilinear detector array;

FIG. 11 shows the projection of multiple angled detector array positionsonto a single virtual curved equiangular detector array; and

FIG. 12 is a schematic diagram of an x-ray scanning system having agantry positioning apparatus mounted to a cantilevered O-shaped gantryand a mobile cart.

DETAILED DESCRIPTION OF THE INVENTION

A description of preferred embodiments of the invention follows.

Referring to FIG. 1, equilinear and equiangular detector geometries aredepicted. A radiation source 13 projects radiation onto multipleone-dimensional linear or two-dimensional planar area detector arrays 14that are angled generally along line or a circle. The detector arraysgenerate scan data from a plurality of diverging radiation beams, i.e.,a fan beam or cone beam. The source and detectors are rotated around theobject to be imaged, and a plurality of projection images is captured tocomputer memory for tomographic projection image processing.

In the case of an equilinear geometry, a single source produces a fan orcone beam which is read by a linear 1D or 2D array of detectors, asshown on the left. In the case of an equiangular geometry, such as shownon the right, the detectors occupy a 1D arc to image fan beam data, or a2D cylindriacal surface to image cone beam data.

Referring to FIGS. 2-3, an equilinear detector geometry is more clearlydefined. As shown in FIG. 2, the detector elements in an array arearranged with constant spacing along a straight line or a flat plane.The angle between rays connecting the x-ray source point and thedetector elements does not remain constant. A radiation absorptionprofile, or image, is generated with varying amplitudes for a regionbetween the bank of detectors and the x-ray source, as shown in FIG. 3.Each ray is identified by its distance, s, from the projection of thecentral ray (s=0), and the absorption profile is denoted by the functionR_(β)(s).

FIGS. 4-5 illustrate an equiangular detector geometry. As illustrated inFIG. 4, the detector elements in an equiangular array are arranged withconstant angular spacing along a circle or cylinder. In an equiangulargeometry, in contrast to equilinear geometry, the angle between raysconnecting the x-ray source point and the detector elements remainsconstant, but the distance between detectors may change. FIG. 5 showsthe radiation absorption profile for the region between the bank ofdetectors and the x-ray source. Each ray is identified by its angle, γ,from the central ray, and the absorption profile is denoted by thefunction R_(β)(γ).

In many radiation imaging applications, it is desirable to image objectsthat are wider than the field-of-view of the detector array. One methodfor achieving a wide field-of-view is to use multiple 1D or 2Ddetectors, arranged end-to-end and angled relative to one another, asshown in FIG. 6. Another technique is to use a single array, translatedto discrete positions along an arc opposite the x-ray source, to obtaina large “effective” field of view. In either case, when one or moreequilinear 1D linear fan beam or 2D planar cone beam detector arrays arepositioned and angled along an arc opposite the x-ray source, theresulting geometry is neither equilinear or equiangular. As illustratedin FIG. 6, the projection of equally spaced detector elements, d_(j), onthe angled arrays do not project onto equally spaced detectors, p_(j),located on lines, planes, or arcs. For example, assuming the detectorelements on the tilted arrays are equally spaced, the process ofreprojecting these elements onto a new virtual detector array which iscoincident or parallel to the central detector array will result inprojections that are not equidistant. Hence, assuming the Fouriertransform filtering is performed continuously along the axes of theangled arrays without resampling, the spacing of detector arrays cannotbe assumed to be equal.

FIG. 7 shows in more detail the result of filtering on non-equallyspaced detectors. The predicted radius of a reconstructed object, R_(r),is calculated on an angled detector geometry, assuming filtering isperformed without resampling onto an equilinear array. If we assume thatthe scanner focal length, FL, is 1000 mm, and the length of thedetectors, L, is 400 mm, then θ_(r)=2*arctan((L/2)/FL)=0.395 rad=22.632deg., and R_(r)=(FL/2)*sin θ_(r)=192.31 mm.

FIG. 8 illustrates this same calculation of the predicted radius of thereconstructed object assuming the same input parameters of focal lengthand detector length, but where the detector arrays are arranged in aplane to provide equilinear geometry. Here, θ_(a)=arctan(L/FL)=0.3804rad=21.795 deg., and R_(a)=(FL/2)*sin θ_(a)=185.695 mm. The predictedradius of the angled detector geometry is larger than that of theequilinear detector geometry, and the resultant images with the angleddetector geometry will be distorted geometrically.

This problem can be overcome by reprojecting and resampling the datafrom the angled detector arrays onto a “virtual” equilinear orequiangular array. The algorithm shown in FIG. 9 describes a method ofreconstructing fan beam or cone beam x-ray projection data of an object,where the detector configuration is neither equilinear or equiangular.In particular, the algorithm describes a method for generating a newvirtual equilinear or equiangular fan beam or cone beam detector arraywhich is defined along a straight line or generally along an arc. Forevery pixel defined in the virtual detector array, the projection pointin the original projection data is determined and the x-ray absorptionamplitude for that point is calculated by interpolating the nearestneighbor pixels. Once resampling is completed, standard filteredbackprojection and algebraic reconstruction techniques may be performedto generate image data. The method consists of creating a single virtualdetector array for each projection position, which is defined as beingequilinear or equiangular, and reprojecting two more real detectorarrays onto the virtual array. Once the real projection data isreprojected onto the virtual detector, the data is filtered andbackprojected using standard tomographic reconstruction techniques;

As shown in step 101 of FIG. 9, the projection angle index, iproj, isfirst assigned the value 1. At step 102, the x-ray source and detectorarray(s) are moved to a projection angle relative to the object beingimaged. This can be accomplished by either moving the source anddetector relative to a stationary object (preferably by moving thesource and detector in a circle or arc around the object), or by keepingthe source and detector stationary and rotating the object to thedesired projection angle.

The projection data can obtained for a plurality of projection angles (1. . . nproj), preferably at a plurality of equally spaced angles as thesource/detector and object are rotated 360 degrees with respect to eachother.

At step 103, a new virtual equilinear or equiangular array, P, isallocated. The virtual array, P, includes virtual pixels which areequally spaced in distance along a line or plane in the case of avirtual equilinear array, or equally spaced in angle along an arc orcurved plane in the case of a virtual equiangular array.

At step 104, the real projection data, D, from each real detector array(1 . . . ndet) is acquired for the given projection angle, iproj.

For each real detector array, D, the real projection data is thenreprojected onto the virtual array, P, at step 107.

As shown at steps 108-115, the reprojection subroutine includes loopingthrough each virtual pixel in the virtual array, P, (step 109), and foreach virtual pixel, determining the real detector pixel, d, that isintersected by the line connecting the virtual pixel and the x-raysource (step 111).

Once this actual pixel, d, is determined, an interpolation techniquethen is applied to d and its nearest neighbors on the real detectorarray to compute an x-ray absorption amplitude value to be assigned tothe virtual pixel, p (step 112). This process is repeated untilabsorption amplitude values have been assigned to each of the virtualpixels in the virtual array.

Once each of the real detector arrays has been projected onto a virtualequilinear or equiangular array, data from the virtual detector array isthen filtered at step 117 and backprojected at step 118. As the nameimplies, there are two steps to the filtered backprojection algorithm:the filtering step, which can be visualized as a simple weighting ofeach Fourier transformed projection in the frequency domain, and thebackprojection step, which can be seen as the dual, or in a more strictmathematical sense, the adjoint, of projection. Instead of projectingdensity values to a projection value, a projection value isbackprojected, or smeared out, over the image points along the ray. Thisentire process is then repeated for each of the projection angles.

Referring to FIGS. 10 and 11, the process of reprojecting x-rays ontovirtual equilinear and equiangular detector arrays is schematicallyillustrated. In FIG. 10, once actual projection images are captured, anew equilinear virtual detector is allocated and defined along aone-dimensional line in the case that a fan beam geometry, or along atwo-dimensional flat plane in the case of a cone beam geometry. In FIG.11, the images are captured by the actual three-panel detector array,and then a new equiangular virtual detector is allocated. Theequiangular virtual detector is an arc in the case of a fan beamgeometry, and a curved cylindrical surface in the case of a cone beamgeometry. In all of these embodiments, the new virtual array assumesthat detector elements are equally spaced in distance or angle,respectively. For each detector element in the virtual array, theprojected position in the real detector arrays is computed and aninterpolation technique is applied to nearest neighbors on the realarray to compute the correct x-ray absorption amplitude of the object tobe reconstructed. Once the real detector arrays have been projected ontothe virtual detector array, standard filtered backprojection, algebraicreconstruction techniques, and other tomographic imaging algorithms maybe applied to generate image data of an object.

In the examples shown here, the real detector array comprises three flatpanel detectors arranged end-to-end, and angled to approximate an archaving a radius centered on the focal spot of the radiation source. Itwill be understood, however, that the principles of the invention can beused with actual detectors having any number of detector elements,including both 1D line detectors and 2D panel detectors, where thegeometry of the actual detector is neither equilinear or equiangular. Inaddition, the principles of the present invention can be advantageouslyemployed in a system where one or more detectors are movable to variousdiscrete positions along a line or arc relative to the x-ray source,such as described in co-pending U.S. patent application Ser. No.10/392,365, filed on Mar. 18, 2003, the entire teachings of which areincorporated herein by reference. The principles of the present can alsobe used in a system in which the source and detector are tiltable aboutthe focal spot of the source to obtain a larger field-of-view in theaxial direction, such as described in co-pending U.S. applicationentitled “Cantilevered Gantry Positioning Apparatus for X-Ray ImagingSystem” (U.S. patent application Ser. No. 10/645,322), filed on evendate herewith, the entire teachings of which are incorporated herein byreference. FIG. 12 is a schematic diagram showing an x-ray scanningsystem 10 described in U.S. patent application Ser. No. 10/645,322. Thex-ray scanning system 10 includes a gantry 11 secured to a supportstructure, which could be a mobile or stationary cart, a patient table,a wall, a floor, or a ceiling. The x-ray scanning system 10 can be usedto obtain two-dimensional planar or three-dimensional computerizedtomographic (CT) x-ray images of an object, such as a patient. In theembodiment shown in FIG. 12, the gantry 11 is a generally circular, or“O-shaped,” housing having a central opening into which an object beingimaged is placed. It will be understood that various other gantryconfigurations, such as a “C-shaped” gantry, can also be employed. Inone embodiment, the gantry 11 contains an x-ray source (such as arotating anode pulsed x-ray source) that projects a beam of x-rayradiation into the central opening of the gantry, through the objectbeing imaged, and onto a detector array (such as a flat panel digitaldetector array) located on the opposite side of the gantry. The x-raysreceived at the detector can then be used to produce a two-dimensionalor three-dimensional image of the object using well-known techniques.The x-ray source is able to rotate around the interior of the gantry 11in a continuous or step-wise manner so that the x-ray beam can beprojected through the object, and through a common isocenter, at variousangles over a partial or full 360 degree rotation. The detector array isalso rotated around the interior of the gantry, in coordination with therotation of the x-ray source, so that for each projection angle of thex-ray source, the detector array is positioned opposite the x-ray sourceon the gantry. The apparatus is thus able to obtain high-quality x-rayimages of the targeted object in any projection plane over a partial orfull 360 degree rotation.

While this invention has been particularly shown and described withreferences to preferred embodiments thereof, it will be understood bythose skilled in the art that various changes in form and details may bemade therein without departing from the scope of the inventionencompassed by the appended claims.

Also, while the embodiments shown and described here relate in generalto medical imaging, it will be understood that the invention may be usedfor numerous other applications, including industrial applications, suchas testing and analysis of materials, inspection of containers, andimaging of large objects.

1. A method of imaging an object using radiation, comprising: projectinga beam of radiation into a central opening of a gantry, from a sourcelocated at one side of a gantry, the beam being projected through anobject being imaged, and onto at least one real detector array locatedon the opposite side of the gantry; obtaining projection data from theat least one real detector array, the at least one real detector arrayobtaining projection data at two or more positions on the gantry, andhaving a geometry that is neither equilinear nor equiangular;reprojecting the projection data from the at least one real detectorarray having the geometry that is neither equilinear nor equiangularonto a virtual detector array including virtual pixels that are spacedeither equilinearly or equiangularly; and reconstructing the reprojecteddata from the virtual detector array.
 2. The method of claim 1, whereinthe at least one real detector array comprises two or more detectorsconfigured to obtain projection data at two or more positions.
 3. Themethod of claim 1, wherein the at least one real detector arraycomprises at least one detector that is movable to obtain projectiondata at two or more positions.
 4. The method of claim 1, furthercomprising: projecting radiation from a source onto the at least onereal detector array.
 5. The method of claim 4, wherein the radiationcomprises x-ray radiation.
 6. The method of claim 1, wherein the virtualdetector array is equilinear.
 7. The method of claim 1, wherein thevirtual detector array is equiangular.
 8. The method of claim 1, whereinreprojecting the projection data onto a virtual array comprises: foreach virtual pixel, determining a corresponding real detector pixel in areal detector array that is intersected by a line connecting the virtualpixel to the source of projected radiation; and using a radiationamplitude value detected at the corresponding real detector pixel todetermine a radiation amplitude value for the virtual pixel.
 9. Themethod of claim 8, wherein determining a radiation amplitude value forthe virtual pixel comprises interpolating a value from the radiationamplitude values of the corresponding real detector pixel andneighboring real detector pixels.
 10. The method of claim 1, furthercomprising: filtering data from the virtual detector array; andbackprojecting data from the virtual detector array.
 11. The method ofclaim 1, wherein the at least one real detector array comprises at leastone one-dimensional line detector.
 12. The method of claim 1, whereinthe at least one real detector array comprises at least onetwo-dimensional flat panel detector.
 13. The method of claim 1, whereinthe source and the at least one real detector array are rotated aboutthe interior of the gantry in a continuous or step-wise manner.
 14. Asystem for imaging an object using radiation, comprising: a gantryhaving a central opening into which an object being imaged is placed; asource of radiation housed within the gantry; at least one real detectorarray that obtains projection data at two or more positions on thegantry, and has a geometry that is neither equilinear nor equiangular;and a data process for reprojecting the projection data from the atleast one real detector array having the geometry that is neitherequilinear nor equiangular onto a virtual detector array that includesvirtual pixels that are spaced either equilinearly or equiangularly, andfor reconstructing the reprojected data from the virtual detector array.15. The system of claim 14, wherein the source comprises an x-raysource.
 16. The system of claim 14, wherein the at least one realdetector array comprises at least one one-dimensional line detector. 17.The system of claim 14, wherein the at least one real detector arraycomprises at least one two-dimensional flat panel detector.
 18. Thesystem of claim 14, wherein the virtual detector array is equilinear.19. The system of claim 14, wherein the virtual detector array isequiangular.
 20. The system of claim 14, wherein the at least one realdetector array comprises at least two detectors configured to obtainprojection data at two or more positions on the gantry.
 21. The systemof claim 20, wherein the at least two detectors are disposed end-to-end,and angled relative to one another to approximate an arc having a radiuscentered at a focal spot of the source.
 22. The system of claim 14,wherein the at least one real detector array comprises at least onedetector movable to two or more positions on the gantry to obtainprojection data.
 23. The system of claim 14, wherein the virtualdetector array comprises an array of equally-spaced virtual pixels. 24.The system of claim 23, wherein the data process reprojects data byassigning a radiation amplitude value to each virtual pixel based upon ameasured radiation amplitude value of a corresponding real pixel thatintersects a line between the virtual pixel and the radiation source.25. The system of claim 14, wherein the source and the at least one realdetector array are rotatable about the interior of the gantry in acontinuous or step-wise manner.
 26. A system for imaging an object usingradiation, comprising: means for projecting a beam of radiation into acentral opening of a gantry, through an object being imaged, and onto atleast one real detector array located on the opposite side of thegantry; means for obtaining projection data from the at least one realdetector array, the at least one real detector array obtainingprojection data at two or more positions on the gantry, and having ageometry that is neither equilinear nor equiangular; means forreprojecting the projection data from the at least one real detectorarray having the geometry that is neither equilinear nor equiangularonto a virtual detector array including virtual pixels that are spacedeither equilinearly or equiangularly; and means for reconstructing thereprojected data from the virtual detector array.